Understanding Wave Interference: Explaining the Effects of Wave Interaction

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When two waves of the same amplitude and wavelength meet, they can create standing waves through interference. At the midpoint between the waves, a particle will oscillate with double the amplitude of the original waves. The discussion also touches on the nature of photons, questioning whether they move in one dimension or spread out in three-dimensional space. The interaction of waves and their resulting effects are central to understanding wave behavior. Overall, the conversation emphasizes the principles of wave interference and the characteristics of wave motion.
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Hi. Could anyone tell me what would happen if these two waves meet? I would also appreciate it if anyone could explain to me how they arrived at their conclusion.

http://img145.imageshack.us/img145/6854/wavest1.png
 
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A left-travelling wave and a right-travelling wave of the same amplitude and wavelength will form standing waves. Is this a homework problem?
 
Also, I don't see a conclusion, just the waveform drawing.
 
for linear waves, a particle at the midpoint between those waves will oscillate once with twice the amplitude of the original waves.
 
Does a photon move in a 1 dimensional direction, or does it move like a wave covering all 'three dimensional' area as it is emitted. (like all 360 degrees on a paper, only three dimensional)
 
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